Top panel: meridional projection for three orbits within the logarithmic potential (Sect. 3.2) with L_z = 8.5 and ΔE = 0.2. Zero velocity curve and some coordinate curves of the elliptic coordinates (with z₀ = 5.9) are drawn. Middle panel: analytical determination of the envelopes of the orbits. Bottom panel: surfaces of section for the same three orbits. Black crosses: numerically computed orbits. Red lines: the corresponding sections obtained from Eqs. (1)−(3). Blue line: surface of section of the orbit confined in the mid-plane (i.e. v_z = 0).